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Renewable Energy 142 (2019) 497e510

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Design, modelling, energy and exergy analysis of a parabolic cooker

Anthony O. Onokwai a, *, Ugochukwu C. Okonkwo b, Christian O. Osueke a,Christian E. Okafor b, Tajudeen M.A. Olayanju a, Samuel, O. Dahunsi a

a Landmark University, Omu-Aran, Kwara State, Nigeriab Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

a r t i c l e i n f o

Article history:Received 9 April 2018Received in revised form5 April 2019Accepted 7 April 2019Available online 24 April 2019

Keywords:DesignEfficiencyMaterialsSolar energyParabolic

* Corresponding author.E-mail address: onokwai.anthony@lmu.edu.ng (A.

https://doi.org/10.1016/j.renene.2019.04.0280960-1481/© 2019 Elsevier Ltd. All rights reserved.

a b s t r a c t

A functional parabolic solar cooker was designed and constructed to serve as an alternate renewablesource of energy for cooking and to also reduce the adverse effects of other sources of energy on theenvironment. The solar cooker was fabricated using cheap, locally sourced available materials in Nigeria.Experimental investigation was carried out on the produced model in Omu-Aran Metropolis, KwaraState, Nigeria in December 2016. Thereafter other investigations were carried out from January toDecember 2017 and lastly in January 2018 between the hours of 10:00 a.m. to 5:00 p.m. local time forboth stagnation and sensible heating, using 2 L of water at every experiment. The average energy andexergy efficiencies of the parabolic cooker were about 39% and 44% respectively. The instability of theenergy efficiency occurred as a result of optical and thermal losses from the reflector and pot, as well asthe varying environmental conditions. Mathematical expressions were used to calculate the theoreticalvalues of energy and exergy efficiencies using Minitab, while the statistical analysis showed that therewas no significant difference between the experimental and predicted results for exergy and energyefficiencies of both cookers at p> 0.05, this validated the design.

© 2019 Elsevier Ltd. All rights reserved.

1. Introduction

Solar energy is outstanding amongst other methods forreducing the utilization of non-renewable resources [1]. With solarenergy, the sun's rays are utilized to heat homes through glasswindows, cook food, charge battery, generate electricity, and heatwater or different fluids [2]. Prior to the emergence of renewableenergy, fossil fuels constitute the primary energy resource that hasbeen used to power human technological advancement, since theindustrial revolution. But there are consequences, for instance,studies show that the high volume of pollutants fossil fuels emis-sions are harmful to public health and environment [3,4,39], whilethe use of fuelwood not only causes deforestation but also loss ofhabitat for millions of species.

Furthermore, in the words of Gardner-Outlaw and Engelman [5]“The search for wood fuel consumes the time, energy and health ofwomen and their children. As local wood supplies grow scarce,women risk spinal cord defect and uterine prolapsed from carryingheavy loads over longer distances. Girls are often requested not to

O. Onokwai).

attain classes in order to help their mothers gather wood forcooking, thereby depriving them of the attendant benefits of edu-cation. Where wood is unavailable, women cook with inefficientfuels such as animal dung or crop wastes, depriving livestock offodder and soils of natural fertilizers. This endangers both thenutritional and respiratory health of women and their families.” Ithas also been emphasized by the World Health Organization(WHO) that 1.6 million deaths per year are caused by indoor airpollution [6]. The dangerous indoor air pollution is not limited torural dwellers utilizing fuelwood but extends to the majority ofurban dwellers that utilize kerosene and gas for cooking. In asmuchas fossil fuel contributes a great deal to the world energy demand,yet the fear of depletion of fossil fuels due to the fast rate of con-sumption has provoked further development of these alternativeenergy sources, such as solar energy [7].

Okafor [8] conducted feasibility Study on the provision of solarenergy in rural area using solar panel; this gave a viable directionfor rural development, while this research focused on thermalenergy for solar cooking. We initiated the research by consideringthe thermal performance of a solar cooker and the weather con-ditions in Nigeria. Firstly, The important of thermal performanceindicators for solar cooker, obtained through exergy analysis wasemphasized by Kumar et al. [9]; while the work of Hereza et al. [10]

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510498

reviewed the principle, classification and parameters affecting thethermal performance of a solar cooker as well as energy and exergyanalysis. Secondly, Osueke et al. [11] investigated the variation inweather conditions stemming from the variation in the amount ofsolar radiation incidents in the different geographical location inNigeria; this had assisted in data analysis and the viability of theresearch which indicates an abundant solar radiant in Nigeria.Thereafter we considered some models.

Petela [12] modelled an exergy analysis of a simple solar para-bolic cooker (SPC), of a cylindrical trough shape, the model allowedfor theoretical estimation of the energy and exergy losses. In otherto improve the performance of a parabolic cooker, Suhail [13],investigated the performance of an improved dual reflector fold-able parabolic solar cooker, while, Harmim et al., [14] and Kaushiket al. [15], designed a novel solar box cooker integrated withcompound parabolic concentrator. A comparative analysis of en-ergy and exergy efficiency of box-type (SBC) and parabolic-typesolar cookers (SPC) was carried out by Ozturk [16], and Pandeyet al., [17]; the results of this study show that therewas a significantdifference between the results of energy and exergy analyses be-tween the two, where SPC shows higher performance at the sametime interval.

In all the literature reviewed, there is inadequate information onthe maximizing locally developed solar cooker in Nigeria. So inNigeria, there is need for the government and private investors toutilize the solar potentials through research and integrate itsapplication into our current energy system. This is necessary asdeveloping solar energy is an appropriate policy for reducing thedependence on imported energy and promoting environmentalprotection in the metropolis [7,41].

The parabolic solar cooker designed and fabricated in this studyused a parabolic-shaped reflector to direct sunlight to a small area(absorber box) in order to generate heat for cooking.

2. Materials and methods

The Parabolic solar box consists of the following components:Parabolic dish, parabolic dish stand, box frame, insulation anddouble wall glass cover. The design was done according toRefs. [2,18]. The cooking vessel (or pot) was placed in a box posi-tioned at the focal point, thus creating a heating condition similarto the conventional open fire cooking. The fabricated cooker wastest ran at Landmark University, Omu-Aran, Kwara State, NorthCentral Nigeria in December 2016. Subsequent tests were carriedout in March, July, November 2017 and January 2018.

2.1. Design calculation

The solar box and parabolic cookers consist of the followingcomponents [19]; Parabolic reflector for the parabola; planereflector for the box cooker; thewooden boxwhich consists of glasscover, absorber and insulator.

2.1.1. Concentrator reflector materialAshby material method was used in selecting the materials for

the parabolic and box cooker.

2.1.2. The shape of the reflector concentrators and the receiversThe design of the shape of the reflector was done according to

Lovegrove et al. [20].

2.1.3. Parabolic dish concentrator sizeThe size of the parabolic dish depends on the solar irradiances

required by the solar cooker. Palavras et al. [21] method was used in

the work.

2.1.4. Aperture area sizeThe total surface area of the solar concentrator uponwhich solar

energy is incident is known as the aperture area of the dish [22],while Ghani [23] defined aperture area as the area that receives thesolar radiation. The sizes of the solar concentrator enhance thecooker's thermal performance.

Therefore, the aperture area was calculated using eqn. (3.1) asstated by Lovegrove et al. [20] and El-Quedermi et al., [24].

Aap ¼ pD2ap

4(3.1)

Aap ¼ 8p3f 2

24 1þ

�Dap�4f

�2!3 =

2

�1

35 (3.2)

¼ 22x0:862

7x4¼ 0:581m2

2.1.5. Solar radiation reflectedThe solar radiation reflected from the concentrator was calcu-

lated using ASHRE [25] empirical model.

IT ¼ Ib þ Id þ Ir (3.3)

The total solar irradiance IT is what remains of extraterrestrialsolar radiation after it had suffered atmospheric extinction. Theempirical forms given by ASHRAE for the components of IT underclear sky are

Ib ¼ Ae�ð Bsin aÞ cosqg (3.4)

Id ¼ ACe�ð Bsin aÞ cosqg (3.5)

Ir ¼�rrcosqrg

�Ae�ð B

sin aÞ cosqr (3.6)

Where: A, B and C are constants determined for average days of themonths.

2.1.6. Focal length of the parabolic dishThakkar et al. [22] defined the focal length (f) as the distance

from the vertex to the focus. The focal length of the focal point fromthe dish concentrator was calculated using Lovegrove et al. [20]equation.

fDap

¼ 14 tanð4rim=2Þ

(3.7)

f ¼ D2ap

16h(3.8)

Where.

f ¼ focal lengthDap ¼ Aperture diameterh¼ depth of the dish (height of the parabola measured from thebase)

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510 499

¼ 8602

16x110¼ 420:23mm ¼ 42:023cm

2.1.7. Size of the aperture receiver areaThe sizing of the aperture area of the receiver was calculated

according to El-Quedermi et al., [24].

As ¼ 8p3f 2

24 1þ

�Dap�4f

�2!3 =

2

�1

35 (3.9)

As ¼ 8x223x7

xð0:381Þ224 1þ

�0:8

=4x0:381

�2!3 =

2

�1

35 ¼ 1:039m2

Arec ¼ Bþ 12p:l ¼ 0:0471þ 1 =2 ð0:016Þx0:16Arec ¼ 0:0484m2

2.1.8. Geometric concentration ratioIt is important to build solar dish with a concentration ratio

greater than 10 [23,26]. Eqn. (3.5) was used to determine theconcentration ratio of the dish as stated by Lovegrove et al. [20].

C ¼ Aap

Aabs(3.10)

C ¼ 0:5810:0484

¼ 12:0

2.1.9. Determination of rim angleThe relationship between focal length with the rim angle and

aperture diameter of the parabolic dish as given by Stine et al. [27],is:

Fig. 1. Plane and sectional draw

4rim ¼ tan�1

264 8f�Dap

16�f�Dap

�2 � 1

375 (3.11)

Where 4rim ¼ Rim angle

4rim ¼ tan�1

24 8x0:42 =0:86

16�0:42 =0:86

�2 � 1

35

4rim ¼ tan�11:387 ¼ :54:2o

The views as well as the dimensions of the parabolic cooker areas shown in Figs. 1e4.

2.2. Material selection

The material selection was based on Ashby's book and it didshed light that material is inherently based on at least 5 inter-related criteria:

� Function of structural component� Materials available and their properties� Shape and size of structural component� Process used to manufacture structural component� Cost and Availability (of both material and process)

Since the aim of the work is to design and fabricate thecomponent, it is imperative that we know the function of all aspectsand the likely materials that can suit the purpose of the functionalarea. We took these functions individually, determined the likelycharacteristics, chose the materials, and their alternates that canserve the function, analysed them and took decision based onqualities, cost and availability of the material.

2.2.1. Parabolic dishThe two materials that had the potentiality to be used as the

parabolic dish was stainless steel and aluminium. From the physicalproperties, stainless steel weighs more with a density of 7.64 g/cccompared to 3.97 g/cc of that of the Aluminium. This makesstainless steel heavier during material handling. Thermally it takes

ing of the parabolic dish.

Fig. 2. Plane and Sectional Drawing of the Collector box.

Fig. 3. Plane and sectional drawing of the dish stand.

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about 100 �C before expansion can occur compared to 20 �C foraluminium. Since the operation does not require very high tem-perature at the parabolic dish. Aluminium stood a better option.Both materials have a considerable polished face and can performthe same action of reflecting the sun's ray.

Aluminium has a “whiter colour,” and loses its lustre faster thanstainless. It also dissipates heat much faster because of its higherconductivity. The two forms of heat transfer involved are Conduc-tion and Radiation. The ability to radiate heat is measured inemissivity. The emissivity of non-published aluminium is around

0.09 while stainless steel 304 is 0.6, which means the lower thevalue, themore the heat reflected. The conductivity of aluminium isabout 145W/m C Stainless steel is 16.26W/m-C [28].

2.2.2. Parabolic dish standMaterials from the African mahogany wood and mild steel were

considered for this project. The modulus of elasticity and thedensity of mild steel is far greater than that of the African ma-hogany wood. We considered the cost per stiffness ratio, stillemploying the Ashby graph, thenwe saw that the cost of wood was

Fig. 4. Designed parabolic cooker in 3D.

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cheaper thanmild steel. But considering other factors like corrosionresistance, availability and workability, mild steel stood out as abetter material [29].

2.2.3. Box frameMost frameworks are done with concrete and plywood when

the thermal conductivity is required to be very small. Looking at therapture of a material, which is defined as the stress in a materialjust before it yields in a flexure test. The concrete has a better andhigher value of 0.00470e0.00600 GPa compared with that ofplywood of 0.0483e0.0689 GPa. This is about 10 times the value ofplywood. Concrete has a higher thermal conductivity than that ofplywood, having a value of 0.750W/m-K compared with0.110e0.147W/m-K of plywood. Since the basic characteristics, welooked at was thermal conductivity. The plywood had moreadvantage than concrete. Additionally, concrete is bulky and wouldcause poor ergonomics during installation and usage due to its lowflexibility [29].

2.2.4. InsulationThe prospective materials are sawdust/wood chipping sand rock

wool. As stated earlier, the major characteristic is the thermalconductivity of the materials in question. Rock wool has a smallerthermal conductivity of 0.0400W/m-K compared to the thermalconductivity of sawdust which is stipulated at 0.110e0.147W/m-K.Another advantage of rock wool is its weight. Rock wool weighs farless than sawdust. This invariably means that the overall weight ofthe box cooker, when integrated with sawdust as the insulatingmaterial, will be higher than when rock wool was used. However,sawdust was chosen as the insulator material because rock woolwas not readily accessible at the time being considered.

2.2.5. Glass coverThe material to use here is glass. This is because from literature.

Glass has been the most consistent material used in the past forsolar applications and transmittance of energy. The surface of aglass is often smooth since during glass formation the molecules ofthe super-cooled liquid are not forced to dispose in rigid crystalgeometries and can follow surface tension, which imposes amicroscopically smooth surface. These properties, gave glass itsclearness, and can be retained even if glass is partially light-absorbingdi.e., coloured. Glass has the ability to refract, reflect, and

transmit light following geometrical optics, without scattering it. Itis used in the manufacture of lenses and windows. Common glasshas a refraction index around 1.5. This may be modified by addinglow-density materials such as boron, which lowers the index ofrefraction (see crown glass), or increased (to as much as 1.8) withhigh-density materials such as (classically) lead oxide (see flintglass and lead glass), or in modern uses, less toxic oxides of zirco-nium, titanium, or barium. These high-index glasses inaccuratelyknown as “crystal” when used in glass vessels causes more chro-matic dispersion of light, and are prized for their diamond-likeoptical properties.

According to Fresnel equations, the reflectivity of a sheet of glassis about 4% per surface (at normal incidence in air), and thetransmissivity of one element (two surfaces) is about 90%. Whenconsidering the thermal strain, the Ashby chart for assessingthermal distortion can be employed. The contours show the valueof the ratio l/a (W/m). Materials with a large value of this designindex show small thermal distortion. They define the guideline.With glass having its C value close to 107, thermal distortion will isminimal [28].

2.3. Construction of the cooker

The solar parabolic dish collector is made from a 0.5mm thickAluminium sheet to reduce heat loss. A manual sun trackingmechanism made of iron bars was also incorporated to constantlyadjust the cooker to the sun's direction. Thin linings of Aluminiumfoil paper were used as the reflector on the outer surfaces of thedish [30]. The bottom of the box is made of China plane wood ofthickness 1/4 in (0.635 cm). The inner surfaces of the box werelined with Aluminium foil. The solar absorber is made from0.54mm thick smooth Aluminium sheet. The Aluminium sheet inthe box is painted matte black to form the absorber. The cookingpots are also painted matte black. The box is constructed in theform of inverted square pyramidal frustum. It is obvious from thefigure that the length of the slanting sides of the absorber isffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi152 þ 7:52

p¼ 16:77 cm. The inner base of the wooden box is

covered with helical/spiral shaped wooden chips. The chips arewaste products of chiseling process and sawdust is then poured onthe chips to serve as insulation layer of 5 cm. The contact surfacebetween the cover and the box are lined with rubber materials.

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2.4. Principles of operation

The parabolic solar cooker uses sun energy as the heat source forcooking different kinds of food. Three basic phenomena areemployed in the design and operation of the cooker. These are:

➢ The parabolic dish receives rays of light from the sun and con-centrates it into a double walled absorber box at the focus point.

➢ The box cooker acts as an absorber and converts the solar ra-diation received to heat for cooking [31].

2.5. Experimental set-up and procedure

✓ Tests were started at around 10:00 a.m. and were stopped ataround 5:00 p.m.

✓ The cooker was kept under shading before the start of the testsand brought to receive solar radiation.

✓ Tracking of the cooker was done manually every 10min.✓ Thermocouples were attached to the centre of the bottom

absorber plate during the No-load (stagnation) test and wereimmersed in water during the boiling test.

✓ In the test, 2 L of water divided equally between two identicalpots was used at each start of the Load test (Sensible test).

✓ Campbell Scientific LTD Anatomy of a weather station installedin Landmark University Omu-Aran, Kwara State was used tomeasure the solar radiation, wind speed, direction of the sunand wind direction.

✓ 4 Channel digital data logging thermometer connected to K-Type thermocouple was used to record the ambienttemperature.

✓ Results were recorded every 10min.

2.6. Energy and exergy analysis

2.6.1. Energy analysisEnergy input is given by Ref. [32].

Ei ¼ IavxAap (3.12)

Where Ei is energy input, Isis the average solar radiation and Aap isarea of aperture of solar cookers.

Fig. 5. Temperatures vs. Time during Sta

Also the energy output may be calculated as follows [32].

Eo ¼ MwCw

�Tf � Ti

�dt

(3.13)

Where is Eo is energy output, Mw mass of water, Cw is specific heatof water, Tf is final temperature of water, Ti is initial temperature ofwater, dt is time difference.

Therefore, the ratio of energy output to input is given by

h ¼ EoEi

¼ Energy outputEnergy Input

2.6.2. Exergy analysisThe exergy input of the parabolic cooker can be calculated using

eqn. (3.15) [32].

Exi ¼ Is

"1þ 1

3

�TabTs

�4� 43

�TabTs

�#Aap (3.15)

Ta is the ambient temperature (K). The sun's black body tem-perature of 5762.

K results in a solar spectrum concentrated primarily in the0.3e3.0 mm wavelength Band [33]. Although the surface tempera-ture of the sun (Ts) can be varied on the earth’ surface due to thespectral distribution, the value of 5800 K has been considered for Ts.

While the exergy output can be calculated using eqn. (3.16) [12],Kreith & Kreider [33]; Pandey et al. [17].

Exo ¼Mw:Cw

h�Tf � Ti

�� TaIn

TfTi

idt

(3.16)

The exergy efficiency is obtained using eqn. (3.17) [34,42].

f ¼ ExoExi

¼Mw:Cw

hðTf�TiÞ�TaIn

TfTi

idt

Is

1þ 1

3

�TabTs

�4 � 43

�TabTs

��Aap

¼ ExergyoutputExergyinput

(3.17)

gnation Test on 6th February 2017.

Fig. 6. Temperatures vs. Time during Stagnation Test on 22nd April 2017.

Fig. 7. Temperatures vs. Time during Stagnation Test on 19th June 2017.

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510 503

3. Results and discussion

Figs. 5e10 shows variations in the ambient, chamber, absorberand water temperature during stagnation (no-load test) and sen-sible heat (load tests) carried out in Landmark University, Omu-aran, Kwara State. The change in the temperature was due to var-iations in solar radiation. The least temperature recorded for stag-nation test was 118.2 �C. This temperature is higher than 100 �C,thus, the cooker can be recommended for drying crops, cooking andheating purpose. Food can be cooked below 111 �C such as Grains(100e110 �C), seafood (63 �C), Beef, Pork, Veal, Turkey and Chicken(71 �C), Eggs(71 �C) [35], while Crops are dried at a temperaturebelow 100 �C [36]. It was observed that the temperatures of thecookers increased gradually as the time increased until it got to apeak level of around 12:30e1: 30 p.m. local time. Also, the timetaken to boil thewater was 105min. The delay in boiling time is as a

result of poor weather and instability in solar radiation. It was alsoobserved that the time taken to boil the water was faster in theMonth of March compared to the month of January, July, Octoberand December. The gradual reduction in sensible temperatures canbe attributed to deterioration (Scratches of the foil, dirt, weaknessof the joints) of the cookers with time [37,40].

The Energy and Exergy Efficiencies plotted based on 8 h sensibletests carried out on March 2017. Further reading was taken in July,October and December 2017. And lastly January 2018 are shown inFigs. 11e13. The energy and exergy efficiencies of parabolic cookerdecrease gradually as the temperature difference/time increaseduntil there was little or no energy and exergy in the cooker around5:00 p.m. local time. The peak energy efficiency for the Month ofMarch, July and October are 43.2%, 33.7% and 40.1% respectively,while the exergy efficiencies are 39.7%, 30.7% and 36.4% respec-tively. The maximum energy and exergy efficiencies occurred

Fig. 8. Temperatures vs. Time during Sensible Test on 15th December 2016.

Fig. 9. Temperatures vs. Time during Sensible Test on 4th January 2018.

Fig. 10. Temperatures vs. Time during Sensible on 6th January 2018.

Fig. 11. Energy and Exergy Efficiency against time of Parabolic Solar Cooker 8th March 2017.

Fig. 12. Energy and Exergy Efficiency against time of Parabolic Dish Cooker 20th July 2017.

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510 505

around 12:30e1:30 p.m. local time. The energy and exergy effi-ciencies were higher in themonth ofMarch compared to theMonthof July, and October due to the increase in solar irradiance andclearness of the sky during the period of the test. The decrease inefficiencies of the cookers is due to deterioration of the aluminiumfoil used as the reflector causing poor reflector of rays (radiation)into the absorber box and myth of overcast sky, while the fluctu-ation in efficiencies was as a result of fluctuating nature of solarradiation [16]. The decrease in energy efficiency of the cookers wasattributed to the optical and thermal losses from the reflector andpot, while the reduction of exergy efficiency of the cooker is due toentropy increase of the cooker together with its surrounding andirreversibility in the cooker caused by empty space minimizationand thermal inertial effect [22].

It was deduced that the exergy efficiency is lower compared tothe energy efficiency mainly due to large exergy of the escaping

insolation and additionally due to the degradation of the insolationabsorber on the surface of the reflector and the cooking pot as seenin Figs. 11e13. The sudden drop in energy and exergy efficiencies asshown in Figs.12 and 18was attributed to variations in atmosphericconditions such as total amount of water vapour in the air, turbidityand increase in significant levels of cloud cover. The decreases werealso caused by changes in the position of the sun.

Fig. 14 shows the Pareto graph of energy efficiency of parabolicdish cooker which was used to determine which factor (main orinteracted) should be truncated from the mathematical model. Anyfactor below the 1.964 (5% level of significance) margin line shouldbe truncated from the Design of experiment (DOE). Hence, ABCD,BCD, BD, ABD, C and AC should be truncated.

The main plot shows how individual factors affect the generalefficiency of the system. Fig. 15 indicates that Is plays a very vitalrole as it shows an increase, which increases the general efficiency.

Fig. 13. Energy and exergy efficiency against time of parabolic dish cooker 5th October 2017.

Fig. 14. Effects Pareto for Energy Efficiency of Parabolic cooker.

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510506

The reset factors gave its best if their values are reduced.Just like the main plot, the interaction plot shows how the ef-

ficiency was affected when two factors were brought together toplay a role as shown in Fig.16. It can be deduced from the figure thattwo factors have a great effect on the energy efficiency of the boxcooker. Solar irradiance & Time, its interaction possessed thehighest interactions factor for energy efficiency.

Fig. 17 shows the graphical representation of the interaction plotshowing how two factors play their effect on the general efficiencyof the system.

Figs. 18e20 shows the mathematical model of Energy andExergy behaviour with time as a result of temperature difference.The predicted results were obtained from the mathematicalexpression derived from the design of experimental using Minitabsoftware. The model equations can reproduce the experimental

results, without necessarily performing an experiment. The energyand exergy results of the cookers gathered during sensible testwere compared using descriptive and inferential statisticalmethods. One-way Analysis of Variance (ANOVA) was carried out at5% significance level to evaluate significant differences between theparabolic and solar box cooker throughout the period of this test.Further statistical analysis using one factor or one-way analysis ofvariance shows that there was no significant difference observedbetween the experimental and predicted results obtained forexergy and energy efficiencies of both cookers as p> 0.05. Thismeans that the mathematical models were able to simulate andreproduce the experimental data, thereby making the modelresponsive. Also, the parabolic and box cookers possessed the samebehaviour and the mathematical model used in describing theperformance of the cooker is correct.

Fig. 15. Main effect plot for energy efficiency of parabolic dish cooker.

Fig. 16. Interaction plot for energy efficiency of parabolic dish cooker.

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510 507

Fig. 17. Contour plot for energy efficiency of parabolic dish cooker.

Fig. 18. Experimental and Predicted Energy Efficiency for parabolic dish cookers on24th July 2017.

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510508

4. Conclusion

A solar cooker was fabricated to help reduce the problemsassociated with cooking fossil fuels (fuelwood, kerosene and gas)which border on environmental impact, health, cost and safety.This work anchored the need to solve these problems using locallybuilt cheap technology that is powered by free available energyresource (solar) in Nigeria. The parabolic cooker was designed andconstructed using local sources materials in Nigeria. Proper selec-tion of materials was carried out to ensure optimum performance.An experimental investigation was carried out on the producedmodel in Omu-Aran Metropolis, Kwara State, Nigeria in December

2016. Thereafter other investigations were carried out from Januaryto December 2017 and lastly in January 2018 between the hours of10:00 a.m. to 5:00 p.m. local time for both stagnation and sensibleheating, using 2 L of water at every experiment. During the no-loadtest, maximum stagnation temperature recorded was 121.7 �C,which is higher than 100 �C, thus, the cooker can be recommendedfor drying crops, cooking and heating purpose [38]. While the peaktemperature obtained during load-test (sensible test) by the para-bolic solar cooker was 100 �C between the hours of 12:30 noon and1:30 p.m. local timewhich basically represents the ideal time to usethe cooker. The cooker is recommended for pre-heating process asthe water can retain higher temperature than the absorber duringcooling process meaning that the interval of sterilization can beprolonged in the cooker. The variation in temperature is attributedto roughness in the foil, dirt, and increase in wind speed and mythof overcast skies. The delay in boiling time is as a result of poorweather and instability in solar radiation. The energy efficiency ofparabolic and box cooker are 44.2 and 39.5% respectively, whiletheir exergy efficiency is 41.3 and 38.3% respectively for sensibleheating of 1 L of water. Also in case of 2 L of water is 35.6 and 30.1%respectively. The parabolic cooker is more efficient than the solarbox cooker as it possessed greater exergy and energy efficiency.Also, it can be observed from the experimental results that thecookers can perform effectively in the month of March than themonth of January, April, July, November and December due to theincrease in solar irradiance and clearness of the sky during theperiod of March.

Design of Experiment was used to obtain mathematical ex-pressions which were used to calculate the theoretical values ofenergy and exergy efficiencies using Minitab and excel solvers.Statistical analysis using one-way analysis of variance shows that

Fig. 19. Experimental and Predicted Energy Efficiency for Parabolic Dish cooker on 3rd December 2017.

Fig. 20. Experimental and Predicted Energy Efficiency for Parabolic Dish cooker on 14th January 2018.

A.O. Onokwai et al. / Renewable Energy 142 (2019) 497e510 509

there was no significant difference between the experimental andpredicted results for exergy and energy efficiencies of both cookersat p> 0.05 showing that the mathematical model was valid. Also,the interactive plot obtained from the predicted energy and exergyefficiency shows that solar irradiance and time, as well as sensibletemperature and time, have a great effect on the exergy and energyefficiency of the cooker.

Conflicts of interest

Authors declare that there is no conflict of interest whatsoever.

Acknowledgement

Authors wish to appreciate the efforts of Landmark UniversityTechnical staff for their immense contributions to the success ofthis work.

Appendix A. Supplementary data

Supplementary data to this article can be found online athttps://doi.org/10.1016/j.renene.2019.04.028.

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